We consider deterministic infinite horizon optimal control problems with nonnegative stage costs. We draw inspiration from learning model predictive control scheme designed for continuous dynamics and iterative tasks, and propose a rollout algorithm that relies on sampled data generated by some base policy. The proposed algorithm is based on value and policy iteration ideas, and applies to deterministic problems with arbitrary state and control spaces, and arbitrary dynamics. It admits extensions to problems with trajectory constraints, and a multiagent structure.